Singular Perturbation Methods

Singularly perturbed systems are multi time-scale systems that exhibit computational stiffness and obtaining the exact solution is a formidable task. The singular perturbation methods, with twin remedial features of dimensional reduction and stiffness removal, are considered as a gift to control engineers. The singular perturbation methodology (SPM) has an impressive record of applications in a wide spectrum of fields such as circuits, networks, power systems, electromagnetics, fluid mechanics, structural mechanics, soil mechanics flight mechanics, celestial mechanics, geophysics, nuclear-reactor dynamics, oceanography, biology and ecology. Discrete systems are very much prevalent in science and engineering. Hence there is a strong need to study the SPM for discrete control systems. Study of a generalized problem is very important in the sense it provides complete picture of the problem. Accordingly a generalized singularly perturbed multiparemter discrete control system with n parameters is the focus of this study. Individual problems can be studied easily from the generalized study. For example in a 'n' parameter study, n=2 results in the study of a two-parameter problem.